A business manager started his retirement account when he was 30. He regularly deposited $1,000 per month at an average rate of 5% compounded monthly. After 15 years of this, he was transferred to Europe for a period of 5 years in which he was unable to make any payments to his account. When he returned, he resumed his monthly payments to his retirement account, albeit a different amount from the original $1,000 per month for 15 more years. If the interest rate remained at 5% compounded monthly, what would his new monthly payments be in order to attain the savings goal that he originally intended? I need help, please. Thank you very much.
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1- Find the FV of his original plan to save $1,000 per month for 35 years @ 5% comp. monthly:
FV =$1,136,092.43
2-Find the FV of all $1,000 payments that he made in the first 15 years or 180 months:
FV =$267,289.03
3-While he was in Europe, the above amount in (2) kept earning interest @ 5% comp. monthly. We have to find out how much was it worth in that 5-year period.
FV =$343,027.76
4-When he resumed his monthly payments after 5 years, he started with the above balance in (3). Since his original objective was to save $1,136,092.43, then this amount would be the FV. The amount in (3) of $343,027.76 would be his PV, 5% comp. monthly would his interest rate, and 180 months would be his remaining term, then we should be able to solve for his new monthly payments:
Pmt =$1,537.78 - his new monthly payments to his retirement account.
