Question

Derek will deposit $4,181.00 per year for 10.00 years into an account that earns 7.00%. Assuming the first deposit is made 6.00 years from today, how much will be in the account 40.00 years from today?

Derek will deposit $1,707.00 per year for 30.00 years into an account that earns 15.00%, The first deposit is made next year. How much will be in the account 36.00 years from today?

Derek will deposit $1,717.00 per year for 10.00 years into an account that earns 14.00%. The first deposit is made today. How much will be in the account 10.0 years from today?

Derek will deposit $9,577.00 per year for 14.00 years into an account that earns 6.00%, The first deposit is made next year. He has $15,886.00 in his account today. How much will be in the account 44.00 years from today?

Derek will deposit $4,617.00 per year for 27.00 years into an account that earns 13.00%, The first deposit is made next year. How much will be in the account 39.00 years from today?

ROUND TO TWO DECIMAL PLACES

Answer 1

Derek will deposit $4,181.00 per year for 10.00 years into an account that earns 7.00%. Assuming the first deposit is made 6.00 years from today, how much will be in the account 40.00 years from today?

Annuity, A = $ 4,181, N = 10 years, R = 7%

FV of annuity (starting from t = 6 years through t = 15 years) at the end of t = 15th year, FV_t=15 = A / R x [(1+R)^N - 1] = 4,181 / 7% x [(1 + 7%)¹⁰ - 1] =$ 57,766.57

Now, we want the FV at the end of t = 40 years, i.e. FV_t=40 = FV_t=15 x (1 + R)^{(40 - 15)} =  57,766.57 x (1 + 7%)²⁵ = $  313,524.16

Hence the amount in the account at t = 40 years from today will be = $ 313,524.16

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Derek will deposit $1,707.00 per year for 30.00 years into an account that earns 15.00%, The first deposit is made next year. How much will be in the account 36.00 years from today?

Annuity, A = $ 1,707, N = 30 years, R = 15%

FV of annuity at the end of t = 30th year, FV_t=30 = A / R x [(1+R)^N - 1] = $ 1,707 / 15% x [(1 + 15%)³⁰ - 1] =$ 742,109.96

Now, we want the FV at the end of t = 36 years, i.e. FV_t=36 = FV_t=30 x (1 + R)^{(36 - 30)} =  742,109.96 x (1 + 15%)⁶ = $ 1,716,545.44.

Hence the amount in the account at t = 36 years from today will be = $1,716,545.44

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Derek will deposit $1,717.00 per year for 10.00 years into an account that earns 14.00%. The first deposit is made today. How much will be in the account 10.0 years from today?

Annuity, A = $ 1,717, N = 10 years, R = 14%

FV of annuity at the end of t = 10th year, FV_t=10 = A / R x [(1+R)^N - 1] = $ 1,717 / 14% x [(1 + 14%)¹⁰ - 1] = $ 33,202.14

Hence the amount in the account at t = 10 years from today will be = $ 33,202.14

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Derek will deposit $9,577.00 per year for 14.00 years into an account that earns 6.00%, The first deposit is made next year. He has $15,886.00 in his account today. How much will be in the account 44.00 years from today?

Annuity, A = $ 9,577, N = 10 years, R = 6%, PV = $ 15,886

FV at the end of t = 14 years will be, FV_t=14 = FV of PV + FV of annuity at the end of t = 30th year, FV_t=30 =PV x (1 + R)^N + A / R x [(1+R)^N - 1] = 15,886 x (1 + 6%)¹⁴ + 9,577 / 6% x [(1 + 6%)¹⁴ - 1] = 28,449.41 + 126,232.47 = $ 154,681.88

Now, we want the FV at the end of t = 44 years, i.e. FV_t=44 = FV_t=14 x (1 + R)^{(44 - 14)} =$ 154,681.88 x (1 + 6%)³⁰ = $ 888,414.01

Hence the amount in the account at t = 44 years from today will be = $ 888,414.01

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Derek will deposit $4,617.00 per year for 27.00 years into an account that earns 13.00%, The first deposit is made next year. How much will be in the account 39.00 years from today?

Annuity, A = $ 4,617, N = 27 years, R = 13%

FV of annuity at the end of t = 27th year, FV_t=27 = A / R x [(1+R)^N - 1] = $ 4,617 / 13% x [(1 + 13%)²⁷ - 1] = $ 927,281.10

Now, we want the FV at the end of t = 39 years, i.e. FV_t=39 = FV_t=39 x (1 + R)^{(39 - 27)} =$ 927,281.10 x (1 + 13%)¹² = $ 4,019,321.35

Hence the amount in the account at t = 39 years from today will be = $ 4,019,321.35